Mbeumo is expected to be "out for weeks" after picking up a "bad" ankle injury during Wednesday's 2-1 defeat at Brighton.
The 24-year-old is hoping to represent Cameroon at the tournament, which starts on January 13.
Cameroon begin their Africa Cup of Nations campaign against Guinea on January 15, then face Senegal four days later before their final Group C game against Gamia on January 23.
Nations competing at the AFCON two years ago saw players join up with their squads six days before the tournament began, a window which was then reduced from 10 days.
Brentford could therefore be expected to release Mbeumo for the tournament following the FA Cup third round. The Bees host Wolves on January 6.
Thomas Frank said on Thursday: “He rolled his ankle. It is bad — I don’t know how bad. We don’t have the exact number of weeks. He will definitely be out for Saturday [away at Sheffield United] and for weeks.”
When asked whether Mbeumo would be hard to replace, Frank said: “Yes, but it was also hard to replace Ivan [Toney].
“We normally find a way. That’s football and it happens sometimes. We will find a solution. There are other players who can step up.
“We need to do everything we can to recover well, and there is also some bad luck in it. [An injury for] Bryan is just bad luck. He gets caught and rolls his ankle. Very frustrating, of course, but I am a positive guy.
“Football is such a marginal game. Hit the post, inside the post, outside the post, deflection: there are so many things you can’t control, like injuries.”